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Rates for Inductive Learning of Compositional Models

AAAI Conferences

Compositional Models are widely used in Computer Vision as they exhibit strong expressive power by generating a combinatorial number of configurations with a small number of components. However, the literature is still missing a theoretical understanding of why compositional models are better than flat representations, despite empirical evidence as well as strong arguments that compositional models need fewer training examples. In this paper we try to give some theoretical answers in this direction, focusing on AND/OR Graph (AOG) models used in recent literature for representing objects, scenes and events, and bringing the following contributions. First, we analyze the capacity of the space of AND/OR graphs, obtaining PAC (Probably Approximately Correct) bounds for the number of training examples sufficient to guarantee with a given certainty that the model learned has a given accuracy. Second, we propose an algorithm for supervised learning AND/OR Graphs that has theoretical performance guarantees based on the dimensionality and number of training examples. Finally, we observe that part localization, part noise tolerance and part sharing leads to a reduction in the number of training examples required.


Inductive reasoning about chimeric creatures

Neural Information Processing Systems

Given one feature of a novel animal, humans readily make inferences about other features of the animal. For example, winged creatures often fly, and creatures that eat fish often live in the water. We explore the knowledge that supports these inferences and compare two approaches. The first approach proposes that humans rely on abstract representations of dependency relationships between features, and is formalized here as a graphical model. The second approach proposes that humans rely on specific knowledge of previously encountered animals, and is formalized here as a family of exemplar models.


'Degree of confirmation' and inductive logic

Classics

In Schilpp, P. A. (Ed.), The Philosophy of Rudolf Carnap, pp. 270–292. Open Court.


Everything you need to know about wireless charging

PCWorld

Wireless charging is one of the most liberating developments in technology today. Instead of searching for and fiddling with wall warts and cables, or crawling under my desk to reach an AC outlet, I just set my Galaxy S7 Edge smartphone on a special pad to top off its battery. When I need to use the phone or leave the house, I pick up it and go--there's nothing to disconnect or unplug. You can enjoy the same experience, but there are a few pitfalls you'll want to watch out for. The biggest one is that there is more than one wireless-charging standard, so you'll need to know which one your smartphone supports.


The Well-Founded Semantics Is the Principle of Inductive Definition, Revisited

AAAI Conferences

In the past, there have been several attempts to explain logic programming under the well-founded semantics as a logic of inductive definitions. A weakness in all is the absence of an obvious connection between how we understand various types of informal inductive definitions in mathematical text and the complex mathematics of the well-founded semantics. We formalize the induction process in the most common principles and prove that the well-founded model construction generalizes them all.